Model independent analysis of dark matter points to a particle mass at the keV scale

We present a model independent analysis of dark matter (DM) both decoupling ultra relativistic (UR) and non-relativistic (NR) based in the phase-space density D = rho_{DM}/sigma^3_{DM}. We derive explicit formulas for the DM particle mass m and for the number of ultra relativistic degrees of freedom g_d at decoupling. We find that for DM particles decoupling UR both at local thermal equilibrium (LTE) and out of LTE, m turns to be at the keV scale. For example, for DM Majorana fermions decoupling at LTE the mass results m ~ 0.85 keV. For DM particles decoupling NR, sqrt{m T_d} results in the keV scale (T_d is the decoupling temperature) and the m value is consistent with the keV scale. In all cases, DM turns to be cold DM (CDM). Also, lower and upper bounds on the DM annihilation cross-section for NR decoupling are derived. We evaluate the free-streaming (Jeans') length and Jeans' mass: they result independent of the type of DM except for the DM self-gravity dynamics. The free-streaming length today results in the kpc range. These results are based on our theoretical analysis, astronomical observations of dwarf spheroidal satellite galaxies in the Milky Way and N-body numerical simulations. We analyze and discuss the results on D from analytic approximate formulas both for linear fluctuations and the (non-linear) spherical model and from N-body simulations results. We obtain in this way upper bounds for the DM particle mass which all result below the 100 keV range.Comment: 11 pages, 2 figures. Expanded version to be published in Monthly Notices of the Royal Astronomical Societ

PG 1115+080: variations of the A2/A1 flux ratio and new values of the time delays

We report the results of our multicolor observations of PG 1115+080 with the 1.5-m telescope of the Maidanak Observatory (Uzbekistan, Central Asia) in 2001-2006. Monitoring data in filter R spanning the 2004, 2005 and 2006 seasons (76 data points) demonstrate distinct brightness variations of the source quasar with the total amplitude of almost 0.4 mag. Our R light curves have shown image C leading B by 16.4d and image (A1+A2) by 12d that is inconsistent with the previous estimates obtained by Schechter et al. in 1997 - 24.7d between B and C and 9.4d between (A1+A2) and C. The new values of time delays in PG 1115+080 must result in larger values for the Hubble constant, thus reducing difference between its estimates taken from the gravitational lenses and with other methods. Also, we analyzed variability of the A2/A1 flux ratio, as well as color changes in the archetypal "fold" lens PG 1115+080. We found the A1/A2 flux ratio to grow during 2001-2006 and to be larger at longer wavelengths. In particular, the A2/A1 flux ratio reached 0.85 in filter I in 2006. We also present evidence that both the A1 and A2 images might have undergone microlensing during 2001-2006, with the descending phase for A1 and initial phase for A2. We find that the A2/A1 flux ratio anomaly in PG 1115 can be well explained both by microlensing and by finite distance of the source quasar from the caustic fold.Comment: 14 pages, 7 figures, 8 tables, Accepted for publication in MNRA